Probing new physics with the kaon decays $K\to \pi \pi /E$

Abstract

The latest search for the rare kaon decay $K^{+}\to {\pi }^{+}\nu \bar{\nu }$ by the NA62 experiment has produced evidence for it with a branching fraction consistent with the prediction of the standard model. The new result implies that in this decay, with the $\nu \bar{\nu }$ pair appearing as missing energy ($/E$), the room for possible new physics is no longer sizable and that therefore its contributions to underlying four-particle $s\to d/E$ operators with parity-even $ds$ quark bilinears have become significantly constrained. Nevertheless, we point out that appreciable manifestations from beyond the standard model induced by the corresponding operators with mainly parity-odd $ds$ quark bilinears could still occur in $K\to \pi \pi /E$ modes, on which there are only minimal empirical details at present. We find in particular that new physics of this kind may enhance the branching fraction of $K_L\to {\pi }^0{\pi }^0/E$ to values reaching its current experimental upper limit and the branching fractions of $K^{+}\to {\pi }^{+}{\pi }^0/E$ and $K_L\to {\pi }^{+}{\pi }^{-}/E$ to the levels of $10^{-7}$ and $10^{-6}$, respectively. Thus, quests for these decays in existing kaon facilities such as KOTO and NA62 or future ones could provide valuable information complementary to that gained from $K\to \pi /E$.

15 pages, no figure, kaon mixing constraint included, references added, matches publication

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• Quark Flavor Phenomenology of the QCD Axion
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• An investigation of the very rare $K^{+}\to {\pi }^{+}\nu \bar{\nu }$ decay
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Cited by in corpus (7)

• FCNC $B$ and $K$ Meson Decays with Light Bosonic Dark Matter
• New physics in $s\to d$ semileptonic transitions: rare hyperon vs. kaon decays
• FCNC charmed-hadron decays with invisible singlet particles in light of recent data
• Light dark-matter window constrained by \boldmath$K^{+}\to {\pi }^{+}$$+$$/E$
• ${\Sigma }^{+}\to p{\ell }^{+}{\ell }^{-}$ decays within the standard model and beyond
• Search for $K_S^0$ invisible decays
• New Physics Searches at Kaon and Hyperon Factories